In (tan (x)) dx. 3. Evaluate J sin(x) cos(x)

Q: a) Find for the following functions: dx i) y = In(x2 + 4) + tanh-1 () ii) x2 cos y + sin 2y = xy %3D…

A: Now we will differentiate with respect to X.  And we  will find dy/dx . Here We will use the formula…

Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. Calculate the following integral: dx (a) sinh? x – 4 sinh x cosh x + 9 cosh² x +*) u (1– x²)² x…

A: 2) a)

Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: Recall that 1, x >0 d (]xl) dx —1, х<0 x < d Use this result and the chain rule to find (sinx|) for…

A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin is…

Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

A: We have to find out solution

Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: Evaluate the following integral. T/2 1 1/4 . sin TX cos 2y sin 2z dy dx dz 0 0 0 T/2 1 1/4 sin TX…

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Q: * = cos(x + y), when x = 0,y = %3D dx

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Q: 1. Find the differential of w = x cos y – y sin x.

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Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: 2m 28. t sin 2t dt

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Q: Pind the derivativa otthe Pollowing の3=2 Sin'Csx) In coshラX 3 =\nx (3) Xsin 4y=Jtan YX

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Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

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Q: Establish the following integration formulas with the aid of residues: cos x - dx xt + 20x² + 64 `

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Q: A-Evaluat wing integrais: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x=2. 3)…

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Q: I. Evaluate the following integrals. (Simplify ) x²dx x3-a³ S sec²(3 – 2x)dx ·cos³ydy 1-siny

A: See the detailed solution below.

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

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Q: 5. Evaluate the integral: Jsin?x cos'x dx

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Q: Use the Beta and gamma function -1 n! 1- Prove that x™(ln x)"dx (m+1)n+1

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

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Q: Q1: Evaluate the following Integration: a) ( In(x²+x)-Inx-en3 dx b) S; sinx Ine(x+1) 1-cos²x

A: Answer (a): To evaluate this integral, apply the logarithmic properties : And, And, And, And,…

Q: Find and show the work for 2 (x+3)(3x+2) dx. (a) (b) SF (sin(2x) – cos x) dx.

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Q: 9. Determine the following antiderivatives: sec?(x) -dx- tan(x) 6. 4x (2x² + 3)°dx а. b. - sin(2x)…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = x/7- x² = Ap %3D

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Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

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Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: The coefficient of sin(x) in the antiderivative of F(x) =| cos 2 %3D

A: Given: F(x)=cosx26

Q: Find the differential and evaluate for the given a and dæ. sin(5z) 1 * = -T. dx 0.75 %3D dy Preview

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Q: y" +Zy+3y=sin (3x)

A: Given that,  y''+2y'+3y=sin(3x) The auxiliary equation is m2+2m+3=0m=-2±4-122=-2±2i22=-1±i2…

Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: II cos(s5) dt ds

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Q: evaluate using Integration by Parts.

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Q: 2х n evaluating J cos²(2x) Tx using integration by parts, identify the portion of the integrand to…

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Q: In the given DE, cos x + In y+ 0, integrating M (x, y) with respect to x generates a function g (y).…

A: To solve the following differential equation

Q: 2.2 Evaluate following integrals. .sin VT cos E 2.2.1 dx

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Q: 1. Evaluate the integral Vi-x² ex?+y*dydx.

A: 1. The given integral is, ∫01∫01-x2ex2+y2dydx. Convert the integral into polar coordinates as…

Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

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Q: RA Find dx dt x In(x) /1 + (In(x))²

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Q: 1. Perform the integration. Show all necessary solutions. 8t² + sin t sint + cos ty dt co t

A: Find your answer below

Q: Q.1 Find the double integral Sle cos x² dA Where R between : x=-y/2, x=1 and y=-2 , y=0.

A: We have to find the double integral

Q: By the even extension method applied to the function f (x) = e-2", where x > 0, the value of the…

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Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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Q: In the given DE, cos x + In y + ( + ev = 0, integrating the coefficient of dx, M (x, y), with…

A: We will find the g(y) as shown below

Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration